Not recorded
This module gives a survey of advanced mathematical methods and their application to problems in physics and more generally, in science and engineering. The aim of the module is to equip students to be well-rounded applied mathematicians, capable of tackling problems using closed-form solutions in certain asymptotic limits.
Topics will be drawn from the following (non-exhaustive) list:
[Review of complex analysis] Cauchy-Riemann conditions, Cauchy's integral theorem, calculus of residues, harmonic functions, Jensen's formula.
[Laplace transforms] Definition, examples, properties, and inversion via the Bromwich contour.
[Asymptotic methods for integrals] Laplace's method, Watson's lemma, steepest-descent method,
[Writing the solution of an ODE as a contour integral] and the evaluation of the same in asymptotic limits where the steepest-descent method can be used; Airy functions.
[Singular perturbation theory] The WKB approximation in the far field and near turning points, applications of WKB theory in Quantum Mechanics and Fluid Mechanics.
[Special functions] Frobenius's theorem, independent solutions, applications involving special functions.
Topics will be drawn from the following (non-exhaustive) list:
[Review of complex analysis] Cauchy-Riemann conditions, Cauchy's integral theorem, calculus of residues, harmonic functions, Jensen's formula.
[Laplace transforms] Definition, examples, properties, and inversion via the Bromwich contour.
[Asymptotic methods for integrals] Laplace's method, Watson's lemma, steepest-descent method,
[Writing the solution of an ODE as a contour integral] and the evaluation of the same in asymptotic limits where the steepest-descent method can be used; Airy functions.
[Singular perturbation theory] The WKB approximation in the far field and near turning points, applications of WKB theory in Quantum Mechanics and Fluid Mechanics.
[Special functions] Frobenius's theorem, independent solutions, applications involving special functions.
About this Module
Student Effort Hours:
| Student Effort Type | Hours |
|---|---|
Not yet recorded. |
|
Requirements, Exclusions and Recommendations
Not applicable to this module.
Module Requisites and Incompatibles
Not applicable to this module.
Assessment Strategy
| Description | Timing | Component Scale | % of Final Grade | ||
|---|---|---|---|---|---|
Not yet recorded. |
|||||
Carry forward of passed components
Not yet recorded
Not yet recorded
| Terminal Exam |
|---|
Not yet recorded |
Not yet recorded